Sign patterns which require or allow the strong multiplicity property
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912374500360192 |
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| author | Saha, Abhilash Tilis, Leona Meulen, Kevin N. Vander Van Tuyl, Adam |
| author_facet | Saha, Abhilash Tilis, Leona Meulen, Kevin N. Vander Van Tuyl, Adam |
| contents | We initiate a study of sign patterns that require or allow the non-symmetric strong multiplicity property (nSMP). We show that all cycle patterns require the nSMP, regardless of the number of nonzero diagonal entries. We present a class of Hessenberg patterns that require the nSMP. We characterize which star sign patterns require, which allow, and which do not allow the nSMP. We show that if a pattern requires distinct eigenvalues, then it requires the nSMP. Further, we characterize the patterns that allow the nSMP as being precisely the set of patterns that allow distinct eigenvalues, a property that corresponds to a simple feature of the associated digraph. We also characterize the sign patterns of order at most three according to whether they require, allow, or do not allow the nSMP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sign patterns which require or allow the strong multiplicity property Saha, Abhilash Tilis, Leona Meulen, Kevin N. Vander Van Tuyl, Adam Rings and Algebras Combinatorics We initiate a study of sign patterns that require or allow the non-symmetric strong multiplicity property (nSMP). We show that all cycle patterns require the nSMP, regardless of the number of nonzero diagonal entries. We present a class of Hessenberg patterns that require the nSMP. We characterize which star sign patterns require, which allow, and which do not allow the nSMP. We show that if a pattern requires distinct eigenvalues, then it requires the nSMP. Further, we characterize the patterns that allow the nSMP as being precisely the set of patterns that allow distinct eigenvalues, a property that corresponds to a simple feature of the associated digraph. We also characterize the sign patterns of order at most three according to whether they require, allow, or do not allow the nSMP. |
| title | Sign patterns which require or allow the strong multiplicity property |
| topic | Rings and Algebras Combinatorics |
| url | https://arxiv.org/abs/2505.08967 |